\[ y''(x)=-\frac {y(x) \sec ^2(x) \left (2 x^2+x^2 \sin ^2(x)-24 \cos ^2(x)\right )}{4 x^2}-\tan (x) y'(x)+\sqrt {\cos (x)} \] ✓ Mathematica : cpu = 0.140711 (sec), leaf count = 46
DSolve[Derivative[2][y][x] == Sqrt[Cos[x]] - (Sec[x]^2*(2*x^2 - 24*Cos[x]^2 + x^2*Sin[x]^2)*y[x])/(4*x^2) - Tan[x]*Derivative[1][y][x],y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{5} c_2 x^3 \sqrt {\cos (x)}-\frac {1}{4} x^2 \sqrt {\cos (x)}+\frac {c_1 \sqrt {\cos (x)}}{x^2}\right \}\right \}\] ✓ Maple : cpu = 0.104 (sec), leaf count = 28
dsolve(diff(diff(y(x),x),x) = -sin(x)/cos(x)*diff(y(x),x)-1/4*(2*x^2+x^2*sin(x)^2-24*cos(x)^2)/x^2/cos(x)^2*y(x)+cos(x)^(1/2),y(x))
\[y \left (x \right ) = \frac {\left (\sqrt {\cos }\left (x \right )\right ) \left (4 x^{5} c_{1}-x^{4}+4 c_{2}\right )}{4 x^{2}}\]